Question

A student wrote the following equations:
3y + 6 = 2x
2y - 3x = 6
The lines represented by these equations are
(1) parallel
(2) the same line
(3) perpendicular
(4) intersecting, but not perpendicular

Answer 1

Using linear function concepts, it is found that the two lines can be classified as:

(4) intersecting, but not perpendicular.

What is a linear function?

A linear function is modeled by:

y = mx + b

In which:

• m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.

• b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

The slope defines if the lines are parallel or perpendicular, as follows:

• If they are parallel, they have the same slope.

• If they are perpendicular, the multiplication of the slopes is of -1.

• If the multiplication of -1, and the slopes are different, they are intersecting.

In this problem, the lines in slope-intercept formula are:

$y = \frac{2}{3}x - 2 \rightarrow = m = \frac{2}{3}$

$y = \frac{3}{2}x + 3 \rightarrow m = \frac{3}{2}$

Then:

$\frac{2}{3} \times \frac{3}{2} = 1$

So they are intersecting and not perpendicular, which means that option 4 is correct.

More can be learned about linear function concepts at https://brainly.com/question/24808124

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